[Haskell-cafe] Newb: List of nodes in a graph - is there a prettier way?

[Torsten Otto]

Howdy,

I'm working towards Dijkstra's algorithm here and I have a feeling  
that I could do without the helper function nodesInternal in the  
following code, if I only could figure out how. Any hints would be  
appreciated.

nodes::Graph->[Id] should (and actually does) return a list of all  
nodes in the graph.

Thanks a bunch in advance.
Regards,
Torsten Otto


 >module Route where

Datatypes for the representation of the graph:

 >type Id = Int
 >type Weight = Int
 >type Edge = (Id,Id)
 >type Graph = [ (Edge, Weight) ]

 >graph::Graph
 >graph =  [ ((0,1),1),
 >			((0,2),3),
 >			((0,4),6),
 >			((1,2),1),
 >			((1,3),3),
 >			((2,0),1),
 >			((2,1),2),
 >			((2,3),1),
 >			((3,0),3),
 >			((3,4),2),
 >			((4,3),1),
 >			((5,2),9)]

 >data Cost = Finite Weight | Infinity
 >			deriving (Eq, Ord, Show)
			
 >type PathCost = (Cost, Id)

Return the number of edges in the graph:

 >edges :: Graph -> Int
 >edges graph = length graph

Calculate the sum of all weights:

 >weightTotal::Graph -> Weight
 >weightTotal ((edge, weight):xs)| xs == [] 	= weight
 >								| otherwise	= weight + (weightTotal xs)
		
List all the nodes in the graph:		
								
 >nodes::Graph -> [Id]								
 >nodes graph = nodesInternal [] graph

 >nodesInternal::[Id]->Graph->[Id]
 >nodesInternal list (((id1,id2),weight):xs)	
 >		| (elem id1 list) && (elem id2 list)		= nodesInternal list xs
 >		| (elem id1 list) && (not (elem id2 list))	= nodesInternal  
(id2:list) xs
 >		| (not (elem id1 list)) && (elem id2 list)	= nodesInternal  
(id1:list) xs
 >		| (not (elem id1 list)) && (not (elem id2 list))	= nodesInternal  
(id1:id2:list) xs
 >nodesInternal list []	= list

Function for adding costs so that we can make use of Infinity for  
impossible routes:

 >addCosts::Cost -> Cost -> Cost
 >addCosts Infinity Infinity		= Infinity
 >addCosts Infinity (Finite x) 	= Infinity
 >addCosts (Finite x) Infinity	= Infinity
 >addCosts (Finite x) (Finite y) = Finite (x + y)

Return the cost of a given edge:

 >lookUp::Edge -> Graph -> Cost
 >lookUp (id1,id2) (((id1x,id2x),weightx):xs)	
 >		| (id1==id1x && id2==id2x)	= Finite weightx
 >		| xs==[]					= Infinity
 >		| otherwise					= lookUp (id1,id2) xs